Question

2cos 2x=7cosx
Помогите пожалуйста !!!!!!!!!)))))))))))

Answer 1

$2\cos 2x=7\cos x\Leftrightarrow -4\sin^2x-7\cos x+2=0\\\cos x=t, |t|\leq 1\Rightarrow 4t^2-7t-2=0\Rightarrow t=\left \{ -\frac{1}{4},2 \right \}\\t=-\frac{1}{4}\Rightarrow x=\pm \left ( \pi - \arccos \frac{1}{4} \right )+2\pi k,k\in \mathbb{Z}$